Variable-Time-Frame Gate-Level Abstraction

1
Variable-Time-Frame Gate-Level Abstraction

• Alan Mishchenko Niklas Een Robert
  Brayton
• UC Berkeley
• Jason Baumgartner Hari Mony Pradeep Nalla
• IBM

2
Overview

• Introduction
• Motivation
• Algorithm
• Experimental results
• Conclusion

3
Abstraction

• Finding a subset of logic gates of the miter,
  large enough to complete the proof

4
Taxonomy of Abstraction Methods

• Automatic vs. manual
• SAT-based vs. BDD-based vs. other
• Proof-based vs. CEX-based vs. hybrid
• Flop-level vs. gate-level
• Fixed time-frame vs. variable time-frame

5
The Proposed Approach is

• Automatic
• SAT-based
• Hybrid
• Gate-level
• Variable time-frame

6
Previous Work

• Flop-level abstraction
• N. Een, A. Mishchenko, and N. Amla, "A
  single-instance incremental SAT formulation of
  proof- and counterexample-based abstraction",
  Proc. FMCAD'10.
• Gate-level abstraction
• J. Baumgartner and H. Mony, Maximal Input
  Reduction of Sequential Netlists via Synergistic
  Reparameterization and Localization Strategies.
  Proc. CHARME05, pp. 222-237.

6
7
Motivation

• Flop-level abstraction is too crude
• Adds too much logic to the abstracted model
• (but refinement with external CEXes is
  easier)
• Gate-level abstraction is also too crude
• Includes all abstracted logic in each time-frame
• Solution Variable-time-frame gate-level
  abstraction
• Adds logic to each time-frames on demand
  (a gate may be added in
  one time-frame but not in others)

8
Improved BMC

• In the classical BMC, in each timeframe, we add
  the complete tent (bounded cone-of-influence)
• experiments show that a small fraction of this
  logic (typically, 5-20) is enough to prove the
  problem UNSAT
• This motivates a smarter approach
• add logic on-demand
• This may reduce the SAT solver size
  substantially, resulting in a faster and more
  scalable BMC

Frame 3
Frame 2
Frame 1
Frame 0
9
Deciding What Logic to Add

• It is enough to add only logic in the UNSAT cores
• But we do not know what is the next UNSAT core
• We use previous cores
• Lift K previous UNSAT cores to the given level
• If the problem is still SAT, refine it by
  selectively adding gates to time-frames
• Use the rollback feature of SAT solver to include
  the minimal amount of logic

UNSAT core of Frame 3
UNSAT core of Frame 2
UNSAT core of Frame 1
UNSAT core of Frame 0
10
Improved Gate-Level Abstraction

• Use the variable-time-frame approach to BMC
• Then, build a gate-level abstraction, by taking
  the union of all gates, present in any time-frame

11
Improved Interpolation

• Interpolation-based model checking can benefit
  from the variable-time-frame approach to BMC
• When the transition relation is unrolled, there
  is no need to add all logic in the COI of the
  property
• The proposed approach can be used to decide what
  logic to include
• As a result
• The SAT problem becomes simpler
• The intermediate interpolants becomes smaller

12
Experimental Results

• abc 01gt read ex1.aig ps
• ex1 i/o 1570/ 1 lat 3113 and 16745 lev
  31
• abc 02gt pdr
• Invariant F29 5033 clauses with 734 flops
  (out of 3113)
• Property proved. Time 808.01 sec
• abc 03gt read ex1.aig ps
• ex1 i/o 1570/ 1 lat 3113 and 16745 lev
  31
• abc 04gt vta -S 5 -P 2 -F 45 -v
• Solver UNSAT 1.49 sec ( 14.50 )
• Solver SAT 2.57 sec ( 24.94 )
• Refinement 5.37 sec ( 52.17 )
• Other 0.86 sec ( 8.37 )
• TOTAL 10.29 sec (100.00 )
• SAT vars 36976. Clauses 92646. Confs 5074.
• Used 0.75 Mb for proof-logging.
• abc 05gt vta_gla ps gla_derive put pdr
• Gate-level abstraction PI 1 PPI 66 FF 143
  (4.59 ) AND 505 (3.02 )

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• abc 02gt r ex1.aig ps
• abc 02gt vta -S 5 -P 2 -F 45 -v
• Frame Confl One Cex All
• 0 0 7 0 6
• 1 0 11 0 11
• 2 0 66 0 80
• 3 0 73 0 31
• 4 0 84 0 135
• 5 0 90 0 61
• 6 0 90 0 71
• 7 0 96 0 100
• 8 0 96 0 116
• 9 0 104 0 152
• 10 0 104 0 174
• 11 0 112 0 219
• 12 0 112 0 249
• 13 0 139 3 323
• 14 0 139 0 360
• 15 0 150 100 555

25 147 617 9 3783 26 2 617
0 3806 27 118 628 22 4581 28
2 628 0 4602 29 144 629 1
5259 30 2 629 0 5290 31 125
635 7 5851 32 2 635 0 5929 33
160 640 1 6549 34 3 640 0
6570 35 212 650 11 7274 36 2
650 0 7295 37 217 650 0 7931 38
3 650 0 7952 39 229 650 5
8519 40 2 650 0 8540 41 295
650 0 9087 42 3 650 0 9109 43
296 650 0 9694 44 2 650 0
9715 SAT completed 45 frames. Time 10.28
sec Solver UNSAT 1.49 sec ( 14.50 ) Solver
SAT 2.57 sec ( 24.94 ) Refinement
5.37 sec ( 52.17 ) Other 0.86 sec (
8.37 ) TOTAL 10.29 sec (100.00 ) SAT
vars 36976. Clauses 92646. Confs 5074. Used
0.75 Mb for proof-logging.
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ABCs vta vs. IBMs SixthSense

• Tried two SixthSense configurations
• Config2 automatic, SAT-based, counter-example-bas
  ed, gate-level, fixed time-frame
• Config5 automatic, SAT-based, hybrid,
  gate-level, fixed time-frame
• Used a suite of 58 model checking benchmarks
  submitted to HWMCC11 by IBM
• Result 1 Config5 produces abstractions that are
  20 (16) smaller in terms of gates (flops)
• Result 2 Config2 completed more timeframes in 5
  minutes for 75 of benchmarks

15
Conclusions

• Reviewed abstraction algorithms
• Motivated an improvement to BMC
• Connected it with gate-level abstraction
• Showed preliminary experimental results

15
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Future Work

• Using coarser objects to abstract, refine, and
  derive CNF
• Adopting min-cut heuristics to decide what gates
  to add to the abstraction
• Performing the initialized unrolling with
  proof-logging